Yeah. In itself that should be particularly difficult, you would hardly need to do more than update the `Dockerfile` and run `docker build` and `docker push`. As I said the way this is setup is currently not ideal, because the Docker image is in my own namespace on Docker hub. There is apparently some resistance to enable the usage of Docker repositories on this GitLab instance, because of storage/bandwidth concerns. I'm not sure what is the best way forward here, but I would argue that having a less-than-ideally setup CI is still better than no CI at all.
The docker image can (and should) be stored on Gitlab. I'd suggest to copy the corresponding scripts from Wine, they already take care of minimizing storage and bandwidth.